A16258 | green_gold_dog, array and permutation

green\_gold\_dog has an array $a$ of length $n$ , and he wants to find a permutation $b$ of length $n$ such that the number of distinct numbers in the element-wise difference between array $a$ and permutation $b$ is maximized.

A permutation of length $n$ is an array consisting of $n$ distinct integers from $1$ to $n$ in any order. For example, $[2,3,1,5,4]$ is a permutation, but $[1,2,2]$ is not a permutation (as $2$ appears twice in the array) and $[1,3,4]$ is also not a permutation (as $n=3$ , but $4$ appears in the array).

The element-wise difference between two arrays $a$ and $b$ of length $n$ is an array $c$ of length $n$ , where $c_i$ = $a_i - b_i$ ( $1 \leq i \leq n$ ).

Each test contains multiple test cases. The first line contains the number of test cases $t$ ( $1 \le t \le 4 \cdot 10^4$ ). The description of the test cases follows.

The first line of each test case contains a single integer $n$ ( $1 \le n \le 4 \cdot 10^4$ ).

The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $1 \le a_i \le 10^9$ ).

It is guaranteed that the sum of $n$ over all test cases does not exceed $4 \cdot 10^4$ .

For each test case, output $n$ numbers - a suitable permutation $b$ . If there are multiple solutions, print any of them.